Global Interfacial Wave Instability of Dendritic Growth from a Pure Melt

2017 ◽  
pp. 129-210
Author(s):  
Jian-Jun Xu
Keyword(s):  
Dendritic Growth ◽  
Interfacial Wave ◽  
Wave Instability

Interfacial wave theory for oscillatory finger formation in a Hele–Shaw cell: a comparison with experiments

1996 ◽  
Vol 7 (2) ◽  
pp. 169-199 ◽  
Author(s):  
Jian-Jun Xu
Keyword(s):  
Wave Theory ◽  
Quantitative Agreement ◽  
Instability Mechanism ◽  
Interfacial Wave ◽  
Wave Instability ◽  
Viscous Fingers ◽  
Theoretical Predictions ◽  
Finger Tip ◽  
Hele Shaw Cell ◽  
Comparison With Experiments

This paper is devoted to an analysis of the formation of oscillatory viscous fingers in a Hele-Shaw cell on the basis of the interfacial wave theory, previously established for the pattern formation dynamics in dendrite growth, as well as in the classic Saffman–Taylor flow. In particular, we study the problem of selection and persistence of oscillatory fingers with a tiny bubble at the finger tip. We obtain uniformly valid asymptotic solutions for this problem, and derive the linear, global wave instability mechanism for this more complicated system. The global, neutrally stable modes are computed in a large region of parameters, which select the form of oscillatory fingers in the later stage of evolution. We have compared the theoretical predictions with the experimental data by Couder et al. (1986) and by Kopf-Sill & Homsy (1987), and found excellent quantitative agreement.

Three-dimensional interfacial wave theory of dendritic growth: (I). multiple variables expansion solutions

2009 ◽  
Vol 18 (2) ◽  
pp. 671-685 ◽  
Author(s):  
Chen Yong-Qiang ◽  
Tang Xiong-Xin ◽  
Xu Jian-Jun
Keyword(s):  
Dendritic Growth ◽  
Three Dimensional ◽  
Wave Theory ◽  
Interfacial Wave ◽  
Multiple Variables

Interfacial wave theory of two-dimensional dendritic growth with anisotropy of surface tension

1991 ◽  
Vol 69 (7) ◽  
pp. 789-800 ◽  
Author(s):  
Jian-Jun Xu
Keyword(s):  
Surface Tension ◽  
Dendritic Growth ◽  
Wave Theory ◽  
Two Dimensional ◽  
Interfacial Wave ◽  
Selection Condition ◽  
Tip Velocity

In this paper, we consider two-dimensional dendritic growth from pure melt with inclusion of the anisotropy of surface tension. The interfacial wave theory previously established for axisymmetric dendritic growth is extended to this case. The results show that the effect of the anisotropy of surface tension on the selection condition of the tip velocity is not significant.

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